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All entries of the matrix of the example but one are non-negative.
The relationship matrix of the example trees is given in Table 1.
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Top: the standard covariance matrix of the 62001 examples extracted from "Barbara" (a) and "Cameraman" (b), and σ = 20.
Table 3 is a confusion matrix of the query by example when the Euclidean distance was used and 10 nearest samples were retrieved.
Figure 8a-b shows the standard covariance matrix of the 62,001 patch examples extracted from "Barbara" and "Cameraman", respectively, with standard deviation σ = 20.
The sensitivity analysis carried out on the Jacobian matrices of the field examples investigated here has shown that the parameter that can be determined with the superior accuracy is θ (as confirmed from drilling information).
The sensitivity analysis carried out on the Jacobian matrices of the field examples investigated here has shown that the parameter that can be determined with the greatest accuracy is θ (as confirmed from drilling information).
Fig. 3 A second running examples: update method Table 5 Example of parameters and values: Fig. 3 Parameter Values status active, retired education undergraduate, graduate regime partial, full working_hours afternoon, morning Table 6 Matrix φ for the example of Fig. 3 Interation of parameters Status Education Regime Working_hours Φ I 1 x x x λ 8 I 2 x x λ x 8 I 3 x λ x x 8 I 4 λ x x x 8.
Table 9 Intermediate matrix M for the example of Fig. 3 Status Education Regime Working_hours ζ active undergraduate partial afternoon 0 active graduate partial λ 3 retired undergraduate partial λ 3 retired graduate partial afternoon 0 active undergraduate full λ 3 active graduate full afternoon 0 retired undergraduate full afternoon 0 retired graduate full λ 3.
Table 10 Final matrix M for the example of Fig. 3 Status Education Regime Working_hours ζ active undergraduate partial afternoon 0 active graduate partial morning 0 retired undergraduate partial morning 0 retired graduate partial afternoon 0 active undergraduate full morning 0 active graduate full afternoon 0 retired undergraduate full afternoon 0 retired graduate full morning 0.
We could not compare our results with those provided in [ 13] since the models they use, coming from metabolic pathways flux analyses, do not have an integer stoichiometry matrix, however the examples of Table 2 show the feasibility of P-invariant computation by constraint programming for quite big networks.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com